A controlled synthesis of polymeric particles is becoming increasingly important because of emerging applications ranging from medical diagnostics to self-assembly. Centrifugal synthesis of hydrogel microparticles is a promising method, combining rapid particle synthesis and the ease of manufacturing with readily available laboratory equipment. This method utilizes centrifugal forces to extrude an aqueous polymer solution, sodium alginate (NaALG) through a nozzle. The extruded solution forms droplets that quickly cross-link upon contact with aqueous calcium chloride (CaCl2) solution to form hydrogel particles. The size distribution of hydrogel particles is dictated by the pinch-off behavior of the extruded solution through a balance of inertial, viscous, and surface tension stresses. We identify the parameters dictating the particle size and provide a numerical correlation predicting the average particle size. Furthermore, we create a phase map identifying different pinch-off regimes (dripping without satellites, dripping with satellites, and jetting), explaining the corresponding particle size distributions, and present scaling arguments predicting the transition between regimes. By shedding light on the underlying physics, this study enables the rational design and operation of particle synthesis by centrifugal forces.@en